Problem: Solve for $x$ : $5x^2 + 45x + 90 = 0$
Dividing both sides by $5$ gives: $ x^2 + {9}x + {18} = 0 $ The coefficient on the $x$ term is $9$ and the constant term is $18$ , so we need to find two numbers that add up to $9$ and multiply to $18$ The two numbers $6$ and $3$ satisfy both conditions: $ {6} + {3} = {9} $ $ {6} \times {3} = {18} $ $(x + {6}) (x + {3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 6) (x + 3) = 0$ $x + 6 = 0$ or $x + 3 = 0$ Thus, $x = -6$ and $x = -3$ are the solutions.